Lesson 7 | Rational and Radical Functions | 11th Grade Mathematics

Objective

Add and subtract rational expressions.

Common Core Standards

Core Standards

The core standards covered in this lesson

A.APR.D.6 — Rewrite simple rational expressions in different forms; write ^a(x/_b(x) in the form q(x) + ^r(x)/_b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Arithmetic with Polynomials and Rational Expressions

A.APR.D.6 — Rewrite simple rational expressions in different forms; write a(x /b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
A.APR.D.7 — Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Arithmetic with Polynomials and Rational Expressions

A.APR.D.7 — Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Foundational Standards

The foundational standards covered in this lesson

A.APR.A.1

Arithmetic with Polynomials and Rational Expressions

A.APR.A.1 — Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Identify the common denominators of an algebraic expression.
Describe how adding numerical fractions with unlike denominators requires the same process as adding or subtracting rational expressions with variables.
Calculate equivalent rational terms through use of common denominators.
Factor or manipulate expressions in ways such that you will be able to find the least common multiple of two denominators.
Identify domain restrictions on rational expressions.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Find the sum of the following two terms:

$${{3\over{n}}+{8\over{n+1}}}$$

Guiding Questions

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Problem 2

Subtract the following two terms:

$${{4\over{n-1}}-{5+n\over4}}$$

Guiding Questions

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Problem 3

Find the sum of the following two terms:
$${{8+x\over{x^2-6x+8}}+{3-2x\over{x^2-3x-4}}}$$

Guiding Questions

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

Subtract the following two terms.
$${{4r\over{r+3}}-{5\over{r}}}$$

References

EngageNY Mathematics Algebra II > Module 1 > Topic C > Lesson 25 — Exit Ticket

Algebra II > Module 1 > Topic C > Lesson 25 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Add the following two terms.

$${{x-2\over{x+4}}+{3-2x\over3}}$$

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Include problems about domain restrictions as well as radicals and rational exponents to provide consistent review throughout the unit.

EngageNY Mathematics Algebra II > Module 1 > Topic C > Lesson 25 — Problem Set
Kuta Software Free Algebra 2 Worksheets Complex Fractions
Rational Expressions Question Stack

Lesson 6

Lesson 8

Lesson Map

Topic A: Introduction to Rational and Radical Functions and Expressions

Define rational functions. Identify domain restrictions of rational functions.

A.APR.D.6 F.IF.B.5

Identify domain restrictions algebraically for non-invertible functions.

F.BF.B.4 F.IF.C.7.B

Graph and transform square root and cubic root functions.

F.BF.B.3 F.IF.C.7.B

Write rational functions in equivalent radical form and identify domain restrictions of rational and radical functions.

F.IF.B.5 N.RN.A.2

Write radical and rational exponent expressions in equivalent forms.

N.RN.A.2

Multiply and divide rational expressions and simplify using equivalent expressions.

A.APR.D.6 A.APR.D.7

Add and subtract rational expressions.

A.APR.D.6 A.APR.D.7

Topic B: Features of Rational Functions and Graphing Rational Functions

Identify asymptotic discontinuities (also known as infinite discontinuities) and removable discontinuities in a rational function and describe why these discontinuities exist.

A.APR.D.6 F.IF.C.7.D

Identify features of rational functions with equal degrees in the numerator and the denominator. Describe how to calculate features of these types of rational functions algebraically.

A.APR.D.6 F.IF.C.7.D

Identify features of rational functions with a larger degree in the denominator than in the numerator. Describe how to calculate these features algebraically.

A.APR.D.6 F.IF.C.7.D

Identify features of rational functions with a larger degree in the numerator than in the denominator. Describe how to calculate these features algebraically.

A.APR.D.6 F.IF.C.7.D

Analyze the graph and equations of rational functions and identify features. Use features of a rational function to identify and construct appropriate equations and graphs.

A.APR.D.6 F.IF.C.7.D

Describe transformations of rational functions.

F.BF.B.3 F.IF.C.7.D

Topic C: Solve Rational and Radical Equations and Model with Rational Functions

Solve simple radical equations.

A.REI.A.2

Solve radical equations and identify extraneous solutions.

A.REI.A.2

Solve rational equations.

A.APR.D.6 A.REI.A.2 A.REI.D.11

Write and solve rational functions for contextual situations.

A.APR.D.6 A.CED.A.2 N.Q.A.1

Analyze rational and radical functions in context and write rational functions for percent applications.

A.APR.D.6 A.CED.A.2 A.REI.A.2

Rational and Radical Functions

Objective

Common Core Standards

Core Standards

Arithmetic with Polynomials and Rational Expressions

Arithmetic with Polynomials and Rational Expressions

Foundational Standards

Arithmetic with Polynomials and Rational Expressions

Criteria for Success

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Target Task

Problem 1

References

Problem 2

Additional Practice

Lesson Map

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